py-06-numpy-distances

0.667

2/3 tests· math

Challenge · difficulty 3/5

# Pairwise distances (numpy)

Implement **`solution.py`** with:

```python
import numpy as np

def pairwise_distances(points: np.ndarray) -> np.ndarray:
    ...
```

`points` is a 2-D array of shape `(n, d)` (n points in d dimensions). Return an `(n, n)`
array where entry `[i, j]` is the Euclidean distance between point `i` and point `j`.

- The result must be a NumPy array (`np.ndarray`), symmetric, with a zero diagonal.
- Use NumPy vectorization (no Python `for` loops over point pairs).
- Example: for `[[0, 0], [3, 4]]` the result is `[[0, 5], [5, 0]]`.

tests/test_distances.py

import numpy as np
from solution import pairwise_distances


def test_simple():
    pts = np.array([[0.0, 0.0], [3.0, 4.0]])
    d = pairwise_distances(pts)
    assert isinstance(d, np.ndarray)
    assert d.shape == (2, 2)
    np.testing.assert_allclose(d, [[0.0, 5.0], [5.0, 0.0]], atol=1e-9)


def test_symmetric_zero_diagonal():
    rng = np.random.default_rng(0)
    pts = rng.standard_normal((6, 3))
    d = pairwise_distances(pts)
    assert d.shape == (6, 6)
    np.testing.assert_allclose(d, d.T, atol=1e-9)
    np.testing.assert_allclose(np.diag(d), np.zeros(6), atol=1e-9)


def test_matches_bruteforce():
    rng = np.random.default_rng(42)
    pts = rng.standard_normal((5, 4))
    d = pairwise_distances(pts)
    for i in range(5):
        for j in range(5):
            expected = np.sqrt(((pts[i] - pts[j]) ** 2).sum())
            assert abs(d[i, j] - expected) < 1e-9

Proposed solution

```python
import numpy as np

def pairwise_distances(points: np.ndarray) -> np.ndarray:
    sq_norms = np.sum(points**2, axis=1)
    dist_sq = sq_norms[:, np.newaxis] + sq_norms[np.newaxis, :] - 2 * (points @ points.T)
    return np.sqrt(np.maximum(dist_sq, 0))
```

Test output (stdout)

.F.                                                                      [100%]
=================================== FAILURES ===================================
_________________________ test_symmetric_zero_diagonal _________________________

    def test_symmetric_zero_diagonal():
        rng = np.random.default_rng(0)
        pts = rng.standard_normal((6, 3))
        d = pairwise_distances(pts)
        assert d.shape == (6, 6)
        np.testing.assert_allclose(d, d.T, atol=1e-9)
>       np.testing.assert_allclose(np.diag(d), np.zeros(6), atol=1e-9)
E       AssertionError: 
E       Not equal to tolerance rtol=1e-07, atol=1e-09
E       
E       Mismatched elements: 1 / 6 (16.7%)
E       Mismatch at index:
E        [5]: 1.4901161193847656e-08 (ACTUAL), 0.0 (DESIRED)
E       Max absolute difference among violations: 1.49011612e-08
E       Max relative difference among violations: inf
E        ACTUAL: array([0.000000e+00, 0.000000e+00, 0.000000e+00, 0.000000e+00,
E              0.000000e+00, 1.490116e-08])
E        DESIRED: array([0., 0., 0., 0., 0., 0.])

test_distances.py:19: AssertionError
=========================== short test summary info ============================
FAILED test_distances.py::test_symmetric_zero_diagonal - AssertionError: 
1 failed, 2 passed in 0.07s